This document evaluates a multipoint equalization algorithm that combines fractional octave smoothing of impulse responses measured in multiple locations in a room or car. It investigates how the equalization performance is affected by varying parameters like the number of measurement positions and equalization zone size. The algorithm extracts a representative prototype response and inverse filter from the smoothed impulse responses. Tests show the proposed approach achieves better spectral deviation and equalization than a single-point method, and performance decreases but remains effective as the equalization zone is expanded to more distant positions.

1. Evaluation of a Multipoint Equalization System based on
Impulse Responses Prototype Extraction
S. Cecchi1
, L. Palestini1
, P. Peretti1
, L. Romoli1
, F. Piazza1
and A. Carini2
1
DIBET, Universit`a Politecnica delle Marche, Via Brecce Bianche 1, 60131, Ancona, Italy
2
STI, Universit`a di Urbino, Piazza della Repubblica 13, 61029, Urbino, Italy
www.a3lab.dibet.univpm.it
Abstract
In this paper a frequency domain multipoint equalization algorithm, which combines
fractional octave smoothing of measured impulse responses (IRs) in multiple loca-
tions and the extraction of a representative prototype, is presented. The proposed
approach is evaluated considering different methods to combine the IRs for the
prototype extraction, and to obtain the inverse filter for equalization, using sets of
impulse responses measured in realistic environments. With respect to previous
works, the influence on the equalization performance of the number of considered
positions and of the equalization zone size is deeply investigated. Also a compar-
ison with the single point equalization approach is reported. Finally, the multipoint
equalization robustness is evaluated also on positions different from those used for
the equalizer estimation.
1. Introduction
Audio equalizers are used to compensate for speaker placement and environment
characteristics and to enhance the listening experience in relation to the user re-
quirements.
Car Equalization Room Equalization
Fixed Equalization: Fixed and Adaptive Equalization:
Inversion approaches [1, 2, 3]. Inversion approaches;
least mean square approaches.
Single Point Equalization Multi Point Equalization [4, 5, 6, 7, 8, 9]:
Measurement of the CIR Measurement of the room IRs in multiple
in a single location. locations (broader equalization zone).
Recently, the authors presented a multipoint room equalization scheme applied
in the frequency domain, based on the fractional octave magnitude smoothing [10].
Objective of this work
To investigate how the performance of the proposed algorithm is affected by vary-
ing important parameters.
2. Proposed Algorithm
The proposed equalizer is derived from multiple measured IRs and it performs
magnitude equalization only.
Figure 1: Overall scheme of the proposed approach.
The operations performed can be divided in 4 steps:
1. Measurement of the IRs in different positions.
2. After the estimation of the frequency responses by means of FFT of length K,
fractional octave smoothing is performed on the frequency responses
3. A representative response of the room response is derived taking into account
all the smoothed IRs, by using different approaches (Mean, Fuzzy c-means, Me-
dian, Root Mean Square and MinMax).
4. The inverse model of the prototype function is obtained, by using two different
approaches (frequency deconvolution with regularization [11] to avoid excessive
gains especially at high frequencies and a low order all-pole LPC model).
3. Test Setup
Figure 2: Loudspeakers and microphones position in the room (left) and inside the car (right).
Test sessions have been performed both inside a real room and in a high-end
car. IRs have been derived using a logarithmic sweep signal excitation [12]
(fs = 48kHz).
Two measures for testing perfomances:
• the spectral deviation, which gives a measure of the deviation of the magnitude
frequency response away from a flat one [4], considering the single IRs before
and after the equalization;
• the Sammon map [13], which takes into account all the measured IRs at a time
and it is a useful representation of room responses and room response equaliza-
tion.
4. Algorithm validation
4.1 Prototypes and Inversion Algorithm Comparison
• Room test session: Ir2 to Ir9 (Fig. 2) for prototype extraction;
• Car test session: Ir1 to Ir12 (Fig. 2) for prototype extraction;
Car Tests Room Tests
Prototype Inversion SDi SDf ∆SD SDi SDf ∆SD
Mean
Fast Deconv 3.6385 2.8871 0.7513 2,6961 2.5043 0.1918
LPC 3.6385 2.8974 0.7411 2.6961 2.5513 0.1448
Fuzzy C mean
Fast Deconv 3.6385 2.9721 0.6663 2.6961 2.5046 0.1915
LPC 3.6385 2.9767 0.6617 2.6961 2.5514 0.1447
Median
Fast Deconv 3.6385 2.9033 0.7351 2.6961 2.5207 0.1753
LPC 3.6385 2.9001 0.7383 2.6961 2.5538 0.1423
MinMax
Fast Deconv 3.6385 3.1500 0.4885 2.6961 2.5365 0.1595
LPC 3.6385 3.1188 0.5197 2.6961 2.5699 0.1261
RMS
Fast Deconv 3.6385 2.8906 0.7479 2.6961 2.5044 0.1917
LPC 3.6385 2.9007 0.7378 2.6961 2.5513 0.1447
Table 2: Spectral deviations SD and their improvement ∆SD = SDf − SDi.
Figure 3: Room (left) and Car (right) prototypes magnitude spectra: 20 dB shift is added for clarity.
This work was supported by the European Commission as sponsor of the hArtes Project number 035143.

2. Figure 4: IRs third octave smoothed magnitude spectra before (left) and after (right) car equalization
using Mean prototype and Fast Deconvolution inversion algorithm.
4.2 Comparison with Single Point Approach
• Room test session:
1. multipoint equalization: Ir1 to Ir5 (Fig. 2) for Mean prototype extraction;
2. single point equalization: inverse filter derived from the smoothed frequency
response of Ir1 (Fig. 2);
• Car test session:
1. multipoint equalization based on Mean prototype extraction and on Fast decon-
volution inversion algorithm;
2. single point equalization with the inverse filter derived from the smoothed fre-
quency response relative to position 1 (Fig. 2).
Car Tests Room Tests
Method Inversion SDi SDf ∆SD SDi SDf ∆SD
Multi point
Fast Deconv 3.7800 2.5140 1.2660 2.7436 2.6628 0.0808
LPC 3.7800 2.5677 1.2123 2.7436 2.5956 0.1480
Single point
Fast Deconv 3.7800 3.0535 0.7266 2.7436 2.7452 -0.0016
LPC 3.7800 3.1003 0.6797 2.7436 2.6913 0.0523
Table 3: Spectral deviations SD and their improvements ∆SD for single point and multipoint equal-
ization.
Figure 5: Sammon map of equalized room (left) and car (right) impulse responses for multipoint
and single point approaches.
Figure 6: IRs third octave smoothed magnitude spectra after single point (left) and multipoint (right)
car equalization.
4.3 Performance Evaluation and Robustness
• Room test session: different IRs sets for prototype extraction have been con-
sidered, covering an increasing equalization zone size (Test 1, Test 2 and Test
3).
• Car test session: two reference positions, relative to driver and passenger, i.e.
Ir3 and Ir4 (Fig. 2) and different IRs sets for prototype extraction, covering a
variable equalization zone, have been selected for the monitoring of performance
variations (Test 1, Test 2, Test 3 and Test 4).
Ir1 Ir10 Ir11 Ir12 Ir13
Test 1
∆SD 0.0460 0.04337 -0.0108 0.0586 0.02253
∆r 23.2159 66.9885 66.1266 74.2943 30.9115
Test 2
∆SD 0.03525 0.05773 0.01083 0.0576 -0.0006
∆r 32.1049 51.0155 62.0416 36.5028 21.3953
Test 3
∆SD 0.0215 0.2665 0.2335 0.2697 0.2674
∆r 32.1049 51.0155 62.0416 36.5028 21.3953
Table 4: Spectral deviation improvements ∆SD and distance from the origin ∆r for the equalized
reference responses for the room test session.
Figure 7: Sammon map of equalized room responses for test session 1 (left), 2 (center) and 3
(right).
Figure 8: Sammon map of equalized car responses for test session 1 (upper left), 2 (upper right),
3 (bottom left) and 4 (bottom right).
5. Conclusions
• A multipoint fixed equalization approach for car and room environment was pre-
sented, together with extensive test sessions.
• The equalizer is designed in the frequency domain to achieve magnitude spec-
trum equalization.
• Mean technique for prototype definition allows to obtain better results.
• LPC model permits to reduce the computational complexity to the detriment of
slightly inferior performance.
• Considering single point equalization, the proposed method proves to be superior
in terms of achieved spectral deviation and of Sammon map as known for room
equalization problem.
• By taking into account impulse responses with increasing distances from the hot
spot, results show that the performance inside the equalization zone decreases
but the outer positions take advantage of the broader equalization.
Future works will be oriented toward the equalization improvement in multichannel
reproduction system and the evaluation of the system through subjective listening
tests.
References
[1] A. Farina and E. Ugolotti, “Spatial Equalization of Sound Systems in Cars,” 15th International Conference: Audio, Acoustics & Small Spaces, Oct. 1998.
[2] A. Bellini, A. Farina, G. Cibelli, M. Ugolotti, and F. Bruschi, “Experimental Validation of Equalizing Filters for Car Cockpits Designed with Warping Techniques,” 109th
AES Convention, proceedings of, Sept. 2000.
[3] M. Binelli and A. Farina, “Digital Equalization of Automotive Sound Systems Employing Spectral Smoothed FIR Filters,” 125th AES Convention, proceedings of, Oct.
2008.
[4] S. Bharitkar and C. Kyriakakis, Immersive Audio Signal Processing. New York: Springer, 2006.
[5] M. Miyoshi and Y. Kaneda, “Inverse filtering of room acoustics,” Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 36, no. 2, pp. 145–152, Feb.
1988.
[6] S. J. Elliot and P. A. Nelson, “Multiple-point equalization in a room using adaptive digital filters,” J.Audio Eng. Soc., vol. 37, no. 11, pp. 899–907, Nov. 1989.
[7] Y. Haneda, S. Makino, and Y. Kaneda, “Multiple-point equalization of room transfer functions by using common acoustical poles,” IEEE Trans. Acoust., Speech, Signal
Processing, vol. 5, no. 4, pp. 325 – 333, July 1997.
[8] S. Bharitkar and C. Kyriakakis, “A cluster centroid method for room response equalization at multiple locations,” in Proc. 2001 IEEE Work. on Appl. of Signal Process.
to Audio and Acoustics, New Paltz, NY, Oct. 2001, pp. 55 – 58.
[9] I. Omiciuolo, A. Carini, and L. Sicuranza, “Multiple position room response equalization with frequency domain fuzzy c-means prototype design,” 11th International
Workshop on Acoustic Echo and Noise Control, proceedings of, Sept 2008.
[10] S. Cecchi, L. Palestini, P. Peretti, F. Piazza, and A. Carini, “Multipoint equalization of digital car audio systems,” in 6th International Symposium on Image and Signal
Processing and Analysis, Proc. of, Sep. 2009.
[11] O. Kirkeby, H. H. Nelson, P. A., and F. Orduna-Bustamante, “Fast Deconvolution of Multichannel Systems Using Regularization,” IEEE Transactions on Speech and
Audio Processing, vol. 6, no. 2, Mar. 1998.
[12] S. Muller and P. Massarani, “Transfer-Function Measurement with Sweeps,” J. Audio Eng. Soc., vol. 49, no. 6, 2001.
[13] S. Bharitkar and C. Kyriakakis, “Visualization of Multiple Listener Room Acoustic Equalization With the Sammon Map,” IEEE Transactions on Audio, Speech and
Language Processing, vol. 15, no. 2, 2007.
This work was supported by the European Commission as sponsor of the hArtes Project number 035143.